Question: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 7x - 1$ and $ JT = 3x + 27$ Find $CT$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {7x - 1} = {3x + 27}$ Solve for $x$ $ 4x = 28$ $ x = 7$ Substitute $7$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 7({7}) - 1$ $ JT = 3({7}) + 27$ $ CJ = 49 - 1$ $ JT = 21 + 27$ $ CJ = 48$ $ JT = 48$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {48} + {48}$ $ CT = 96$